When a pressure of 100 atmosphere is applied on a spherical ball of rubber, then its volume reduces to 0.01%. The bulk modulus of the material of the rubber in dyne/cm² is

The correct option is 1 x10¹².

To find the bulk modulus of the material of the rubber ball, we can follow these steps:

1. Formula for Bulk Modulus:
The bulk modulus ($K$) is defined as the ratio of bulk stress (change in pressure) to bulk strain (fractional change in volume):
$K=\frac{P}{\left(\frac{\Delta V}{V}\right)}$
where:
$P$ is the applied pressure,
$\Delta V$ is the change in volume, and
$V$ is the original volume.

2. Convert Pressure to CGS Units (dyne/cm²):
The given pressure is:
$P=100\text{atm}$
Since $1\text{atm}\approx {10}^6{\text{dyne/cm}}^2$ (more precisely $1.013\times {10}^6{\text{dyne/cm}}^2$), we can convert the pressure as follows:
$P=100\times {10}^6{\text{dyne/cm}}^2={10}^8{\text{dyne/cm}}^2$

3. Calculate the Fractional Change in Volume (Volume Strain):
The volume of the ball reduces by $0.01\%$. Therefore, the volumetric strain is:
$\frac{\Delta V}{V}=\frac{0.01}{100}={10}^{-4}$

4. Calculate the Bulk Modulus:
Substitute the values of pressure and volumetric strain into the bulk modulus formula:
$K=\frac{{10}^8}{{10}^{-4}}$
$K={10}^{12}{\text{dyne/cm}}^2=1\times {10}^{12}{\text{dyne/cm}}^2$

Thus, the bulk modulus of the rubber material is $1\times {10}^{12}{\text{dyne/cm}}^2$.